Higher Bers maps
type: Item
instance of: scholarly article
title: Higher Bers maps
zbMATH Open document ID: 1256.30035
author: Guy Buss
published in: The Asian Journal of Mathematics
publication date: 2012-06-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/0812.0314
full work available at URL: https://projecteuclid.org/euclid.ajm/1331663453
reviewed by: Alastair Fletcher
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30C55
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 6050965
zbMATH Keywords: Teichmüller spaces
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: higher Schwarzians
zbMATH Keywords: univalent functions
MaRDI profile type: Publication
arXiv ID: 0812.0314
OpenAlex ID: W2962678946
DOI: 10.4310/AJM.2012.V16.N1.A4
review text: The study of Teichmüller spaces is highly topical. A key feature of this theory is that of the Bers embedding. Let \(S\) be a Riemann surface. Then the Bers embedding is a holomorphic map from Teichmüller space \(\mathcal{T}(S)\) to a bounded open subset of the Banach space of holomorphic quadratic differentials on \(S\), equipped with the hyperbolic-supremum norm.NEWLINENEWLINEIn the paper under review, the author studies differential operators on conformal mappings with various other group invariances. In particular, the author gives conditions for such a differential operator to induce a holomorphic map from \(\mathcal{T}(S)\) into a complex Banach space of \(m\)-differentials. The paper contains an extensive survey of the Bers embedding and Teichmüller theory, and concludes by outlining the further work that needs to be done for this approach to have greater impact on Teichmüller theory.
description: scientific article; zbMATH DE number 6050965